The idea that petroleum is always going to be 'fungible' is an economist's fantasy, an article of faith that is not grounded in reality or history or human nature.  On the contrary, when Peak Oil is finally recognized as having already occurred, the people who own (possess,control) petroleum reserves are going to think that they can benefit by taking those reserves off the free market and instead using them to benefit themselves, the owners. We are practically guaranteed to see the phenomenon of nationalization of petroleum reserves.  Everybody will ask themselves 'just what is the true value of petroleum?', and they will rapidly conclude that the true value to their people, their nations, is a lot greater than 68 USD per barrel.  As the previous poster said, the existence of a free market in petroleum is a relatively recent phenomenon.  Up through WW-II, petroleum was thought of by everybody as a special asset that nations either possessed (controlled) or didn't possess (control).  The story of WW-II can be written as the struggle to control petroleum assets.  There was no free market in those days!  Instead of believing in 'fungibility', it would be more prudent to suppose that after Peak Oil the situation will more resemble that of 1939-41, when Germany desperately wanted Caspian petroleum and Japan desperately wanted Indonesian petroleum.
I hope this analogy does not incur any more sandwich shop references, but imagine you are a baker. Normally flour is purchased cheaply, you process it into bread, feed your family and sell as much of the surplus to all your customers who are happy they can buy bread and not make it themselves. What if one day there was a disruption that caused flour to stop coming, or at an extraordinarily high price. No matter what you are still going to feed your family. Maybe you sell one extra loaf (at a very high price) to pay for other essentials. But until the disruption ends, you may just sit on your stockpile of flour as long as possible and deny access to your customers to continue to baking for your family. The same is true of oil producers - they will not sell the oil if their citizens need it. They will sell just enough to afford the other items they need and not more.
This is true for food and families, but not true for food and nations. African nations are frequently exporting food while their people are starving. I imagine oil will work similarly. Most oil reserves are already nationalized - the question is whether the government and national oil companies will want to sell oil cheaper on the internal market than they can get on the external market. Indonesia and China are becoming case studies with what happens under that approach. Black markets and smuggling will limit the ability to do so (as in Iraq).
Obviously if you have an asset which is increasing in price, like oil during a shortage, it's better to own it. Then you will profit (or at least not be hurt) by the increase.

At the same time, economics doesn't go away. If your oil increases from $65/bbl to $200/bbl, people still face the same choice: holding $200 or holding a barrel of oil. This choice applies to equally to people who hold the oil and to people who don't. Owning the oil doesn't make this choice go away.

Generally, absent price controls, the price will rise to the point where (marginal) producers are ambivalent between holding the oil and holding the money. This means that even if you own oil, you're still going to be faced with a hard choice between whether to sell it (i.e. go without the oil but have the money) or keep it (go without the money but have the oil). Exactly the same choice is faced by a buyer: go without the money and have oil, or go without oil and have money.

This is the point of the "oil is fungible" argument, and it applies even if the price rises. Again, of course being an owner is better during the price rise; it's always good to own an appreciating asset. But that doesn't change the fact that you will always be faced with the hard choice: oil or money. Both owners and consumers are in that same situation.